{"title":"用升降投影法通过无穷小发生器对特殊带宽共享模型进行扩散逼近","authors":"Bowen Xie , Yijin Gao","doi":"10.1016/j.orl.2023.107063","DOIUrl":null,"url":null,"abstract":"<div><p>We consider a proposed unsolved conjecture of a special bandwidth-sharing model integrating streamings and file transfers as initiated in Kumar and Massoulié (2007). Using the infinitesimal generator<span> approach, we demonstrate its diffusion approximation with a special time-scale separation parameter. To this end, we introduce a lifting-projection method, and exhibit a novel function to show the generator of a joint process converges to that of a univariate limiting file-transfer process, where the streaming flows are averaged out in heavy traffic.</span></p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"52 ","pages":"Article 107063"},"PeriodicalIF":0.8000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Diffusion approximation of a special bandwidth sharing model via infinitesimal generators with a lifting-projection method\",\"authors\":\"Bowen Xie , Yijin Gao\",\"doi\":\"10.1016/j.orl.2023.107063\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We consider a proposed unsolved conjecture of a special bandwidth-sharing model integrating streamings and file transfers as initiated in Kumar and Massoulié (2007). Using the infinitesimal generator<span> approach, we demonstrate its diffusion approximation with a special time-scale separation parameter. To this end, we introduce a lifting-projection method, and exhibit a novel function to show the generator of a joint process converges to that of a univariate limiting file-transfer process, where the streaming flows are averaged out in heavy traffic.</span></p></div>\",\"PeriodicalId\":54682,\"journal\":{\"name\":\"Operations Research Letters\",\"volume\":\"52 \",\"pages\":\"Article 107063\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Operations Research Letters\",\"FirstCategoryId\":\"91\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167637723002043\",\"RegionNum\":4,\"RegionCategory\":\"管理学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"OPERATIONS RESEARCH & MANAGEMENT SCIENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Operations Research Letters","FirstCategoryId":"91","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167637723002043","RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
Diffusion approximation of a special bandwidth sharing model via infinitesimal generators with a lifting-projection method
We consider a proposed unsolved conjecture of a special bandwidth-sharing model integrating streamings and file transfers as initiated in Kumar and Massoulié (2007). Using the infinitesimal generator approach, we demonstrate its diffusion approximation with a special time-scale separation parameter. To this end, we introduce a lifting-projection method, and exhibit a novel function to show the generator of a joint process converges to that of a univariate limiting file-transfer process, where the streaming flows are averaged out in heavy traffic.
期刊介绍:
Operations Research Letters is committed to the rapid review and fast publication of short articles on all aspects of operations research and analytics. Apart from a limitation to eight journal pages, quality, originality, relevance and clarity are the only criteria for selecting the papers to be published. ORL covers the broad field of optimization, stochastic models and game theory. Specific areas of interest include networks, routing, location, queueing, scheduling, inventory, reliability, and financial engineering. We wish to explore interfaces with other fields such as life sciences and health care, artificial intelligence and machine learning, energy distribution, and computational social sciences and humanities. Our traditional strength is in methodology, including theory, modelling, algorithms and computational studies. We also welcome novel applications and concise literature reviews.